An asteroid is about to fly past the moon (about 384,000km away) and is on a col

Question

An asteroid is about to fly past the moon (about 384,000km away) and is on a collision course with the earth. The mass of the asteroid is about 1.45e20 kg. It approaches earth on a direct impact course with a velocity of about 2.0m/s. You are part of an elite team of experts assigned to find a way to deflect the path of the asteroid. Note: Mass of the earth is about 6e24 kg, and the radius is 6400km.
1) Ignoring the effects of air-resistance, if the total kinetic energy of the asteroid was released in an explosion when it impacts the surface of the earth, what is the TNT equivalent of that energy? 1 ton TNT = 4.184e9 J. 1 megaton TNT = 1Mt = 1e6 t of TNT = 4.184e15 J.
2) If all of this energy can be used to power 7W LED light bulbs for a year, how many such bulbs can you power in total?
3) Your team devised a plan to insert and detonate a nuclear device in the center of the asteroid. Suppose this was done in a timely fashion, so that the asteroid has just past the moon. Your team had calculated that about 60% of the energy will go into splitting the asteroid into two halves of the same mass and that the two halves will begin to move apart along a direction perpendicular to the initial velocity vector with the hope that the two parts will miss the earth. What is the total energy needed in the detonation? How many TNT equivalents do we need? If a typical nuclear bomb yields 50Mt of energy, how many will you need? (For this part, ignore the effects of gravity.)
Bonus) Can you save the earth? Name and explain other effects that we may need to consider in order to do a more accurate calculation.

Explanation / Answer

E=1/2 mv^2 + (-(Gm_1m_2)/r^2)

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